# How do you find the degree of displacement?

1. Sep 5, 2010

### hypoovenmitts

A girl travels 5 blocks west, 4 blocks north, then 7 blocks east. It asked to solve for the magnitude of her displacement and I got 4.472135955 blocks, which was correct. The next part of the problem however asks to "Find the direction (measured from due east, with counterclockwise positive) of her displacement. Answer in units of degrees."

I just began physics last and my teacher didn't go over this. I know the displacement is northwest, but I don't know how to find the degrees of it. Thank you very much!

2. Sep 7, 2010

### Delphi51

It amounts to 2 blocks east and 4 north. Draw a triangle with these sides. Then you just have to find the angle in the triangle (at the beginning, from straight east up to the hypotenuse which you found to be 4.47 long. If your diagram is drawn accurately, you can find the angle with a protractor.

Or you can use trigonometry to find the angle. Here is a very quick rundown on trigonometry:

SOA means sine(angle) = opposite side/adjacent side
CAH means cosine(angle) = adjacent side/hypotenuse
TOA means tangent(angle) = opposite side/adjacent side

You decide which of these three relates sides you know to the angle you want to find (all three work in this case). Figure out the right hand side by dividing, then use the inverse SIN, inverse COS or inverse TAN key on your calculator to get the angle. Careful, advanced calculators may need to be put into degree units to get answers in degrees.